Asked whether he had at any stage spoken with his colleagues about Ms Gillard's leadership, Senator Carr said: ''No''.

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Fairfax Media reported on Tuesday that Senator Carr told colleagues that he had lost confidence in Ms Gillard due to concerns over her leadership and capacity to effectively campaign. A second minister, South Australian Mark Butler, reportedly told colleagues that he was reconsidering his support for the PM.

'I'm loyal to Julia Gillard'' ... Bob Carr briefs reporters in Washington alongside US Secretary of State John Kerry.Credit:AP

Fairfax journalist Peter Hartcher, who wrote the original story, said on Tuesday that Senator Carr's colleagues were ''astonished today to hear him say that the Prime Minister enjoys his full support''.

''Bob Carr has described colourfully and in detail to many of his colleagues his view of the Prime Minister's political judgment,'' Hartcher said, ''starting in November last year when he defied the Prime Minister on the Israel-Palestine vote in the UN''.

Senator Carr's factional colleagues in the NSW Right have known for some time that he was a ''firm supporter'' of Kevin Rudd for the Labor leadership, according to Hartcher.

''His colleagues report that he has been scathing in his criticisms of Ms Gillard's judgment. He was further appalled at Julia Gillard's judgment when she rammed the media reform proposals through the cabinet without telling cabinet ministers about them,'' Hartcher said.

Support ... Julia Gillard.

During Senator Carr's interview with ABC TV on Tuesday morning, he was asked whether he had ever discussed the government's fortunes with his colleagues. Senator Carr replied: ''No, I haven't''.

''Have you expressed reservations,'' Senator Carr was then asked, ''with your close colleagues about how the government's fortunes are playing out?''

''No,'' Senator Carr replied.

''Those stories aren't true,'' he said. ''I'm loyal to Julia Gillard, and Julia Gillard, in my view, will lead the Labor Party to the election in September.''

Hartcher said Senator Carr's claims that he had never discussed Ms Gillard's leadership or the party's fortunes with any of his colleagues would make the Foreign Minister ''unique in the modern Labor Party''.

The other MP at the centre of the leadership speculation, Mark Butler, tweeted on Tuesday morning: ''Still a proud member of Julia Gillard's team, contrary to latest media frenzy.''

Meanwhile, independent MP Tony Windsor has warned the Labor Party that it did not deserve the support of the crossbench if it could not agree on who was stable enough to run the place.

''If they continue with this election mode and this whole business about who the leader is well they might get to an election quicker than the September 14,'' he told ABC Television.

At the press conference earlier with Secretary Kerry, Senator Carr said the Prime Minister had his unqualified support.

''She has my support and I think the media's in a frenzy of speculation - speculation feeding on itself that generates these stories.''

Pressed further on the issue after the formal press conference, Senator Carr said: ''I am not going to feed speculation that feeds on itself and goes very, very silly. I made it very clear up there that I am a strong supporter of the Prime Minster and that what you read is media speculation feeding on itself endlessly.''

He denied he had expressed concerns over Ms Gillard's leadership to colleagues and said he had no designs on the leadership himself.

The question was first put to the Foreign Minister during the press conference after the first bilateral talks between Senator Carr and Secretary Kerry, prompting some laughter from local reporters and State Department staff, who have some experience of the turbulent nature of recent Australian politics.

Senator Carr is staying a few blocks away at the Willard Hotel. It was there in February last year that Kevin Rudd announced his resignation as foreign minister, shocking not only Australians, but many of the State Department staff whose job it was to keep track of Australian politics.

As the two nations' most senior diplomats spoke earlier on Monday in Washington, the Australian ambassador to the US – former Labor leader Kim Beazley - watched on from behind a stand of cameras.

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Mr Beazley would well remember the night in June 2010 when he was called into the office of then US Secretary of State Hillary Clinton, to brief her on the shock removal of Mr Rudd from the role of prime minister.